Concrete mathematics : a foundation for computer science

Next week we’re
getting walls.
3.1 FLOORS AND CEILINGS 69
Thus each is easily expressible in terms of the other. This fact helps to
explain why the ceiling function once had no notation of its own. But we
see ceilings often enough to warrant giving them special symbols, just as we
have adopted special notations for rising powers as well as falling powers.
Mathematicians have long had both sine and cosine, tangent and cotangent,
secant and cosecant, max and min; now we also have both floor and ceiling.
To actually prove properties about the floor and ceiling functions, rather
than just to observe such facts graphically, the following four rules are especially
useful:
1x1 = n w n